5 papers
Low-dimensional adaptation of diffusion models: Convergence in total variation
Jiadong Liang, Zhihan Huang, Yuxin Chen
This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling. Focusing on two mainstream samplers -- the denoising di…
Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees
Daniil Dmitriev, Zhihan Huang, Yuting Wei
Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling effi…
Semiparametric KSD test: unifying score and distance-based approaches for goodness-of-fit testing
Zhihan Huang, Ziang Niu
Goodness-of-fit (GoF) tests are fundamental for assessing model adequacy. Score-based tests are appealing because they require fitting the model only once under the null. However,…
Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality
Zhihan Huang, Yuting Wei, Yuxin Chen
The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI. While sharp convergence guarantees have been established for the D…
Towards a mathematical theory for consistency training in diffusion models
Gen Li, Zhihan Huang, Yuting Wei
Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining s…